Testing a claim at every angle

You will write a tester that checks a claimed identity at every whole angle from $1^\circ$ to $89^\circ$, and use it on a true claim and a false one.

Your tasks.

1. In holds, return True if left(A) and right(A) differ by less than 1e-9 at every whole angle from $1^\circ$ to $89^\circ$, else False. The functions take the angle in radians.
2. In first_failure, return the first whole angle in degrees, from $1^\circ$ up, where the two sides differ. Return None if there is none.
3. Write sec2 and one_plus_tan2 so that holds(one_plus_tan2, sec2) tests $1 + \tan^2 A = \sec^2 A$.